As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships

A and D are the two ships and the distance between the ships is AD. BC is the lighthouse and is the height of the lighthouse. observer is at point C
Give: BC = height of lighthouse = 75m

∠CAB = 45°,

∠CDB = 30°

To Find:  DA

In Δ ABC,

             
[ p = perpendicular and b = base of the right angled triangle]

AB=75 m                        [ tan 45º = 1]

In Δ CDB,

AD + AB= 75√3 m

DA = 75( √3 - 1) m 
Hence the distance between the ships is 75( √3 - 1) m